The earliest opportunity to attempt this is Act 1-3: Giant.
This requires the KNRB-0 Argus to be in it's second (bipedal) form. You need to destroy each of the listed weak spots before finishing the robot off. The legs are also a weak spot but destroying them isn't required. Each of these weak spots can be identified by it's orange glow. After destroying a weak spot the robot will collapse and expose it's core - destroying the core destroys the robot. You can start taking out the core during the collapses to shorten the duration of the fight but do not attack additional weak spots during the collapses as it won't destroy them. When attacking the head you will be prompted with a QTE, completing this does not void the achievement.
An alternative location to attempt this is Act 2-3: Nightmare where you will have to fight two Argus robots in order to unlock the Failure Breeds Success achievement.